411 REFERENCE · Wikibooks
Physics Using Geometric Algebra/Relativistic Classical Mechanics/Spacetime position
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The spacetime position can be encoded in a paravector
with the scalar part of the spacetime position in terms of the time
The proper velocity is defined as the derivative of the spacetime position with respect to the proper time
The proper velocity can be written in terms of the velocity
where
and of course
The proper velocity is unimodular
Spacetime momentum
The spacetime momentum is a paravector defined in terms of the proper velocity
The spacetime momentum contains the energy as the scalar part
where the energy is defined as
The shell condition of the spacetime momentum is